Three nontrivial solutions for nonlinear fractional Laplacian equations

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DÜZGÜN F. G., IANNIZZOTTO A.

ADVANCES IN NONLINEAR ANALYSIS, vol.7, no.2, pp.211-226, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1515/anona-2016-0090
  • Journal Name: ADVANCES IN NONLINEAR ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.211-226
  • Hacettepe University Affiliated: Yes

Abstract

We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three non-zero solutions. When the reaction term is sublinear at infinity, we apply the second deformation theorem and spectral theory. When the reaction term is superlinear at infinity, we apply the mountain pass theorem and Morse theory.